Solving the Tower of Hanoi Puzzle with Heavy Disks - Fried, Sela (The American mathematical monthly, 2025)
The Tower of Hanoi puzzle, traditionally solved with light disks, presents unique challenges when using heavy disks. This study focuses on minimizing the total distance traveled by the disks during the solution process. The puzzle's rules allow flexibility in designating the starting and target pegs, prompting an analysis of optimal configurations. The recursive nature of the puzzle reveals that the total distances, denoted as \(a_n\) and \(b_n\) for different peg arrangements, can be expressed through generating functions. The findings indicate that for even numbers of disks, the choice of target peg does not affect the total distance. However, for odd numbers, selecting peg 2 as the target reduces the distance by one move compared to peg 3. This research not only provides insights into the mechanics of the Tower of Hanoi with heavy disks but also connects to broader mathematical concepts, including the Jacobsthal numbers and their applications in related puzzles.